ECAT Pre Engineering MCQ Test With Answer for Mathematics Full Book

The 7th term of the A.P 7,11,15,is

• 24 A
• 31 B
• 26 C
• 23 D

• 
  A
• 
  B
• 
  C
• 
  D

Three points whose position vector a,b,c are collinear

• axb +b x c+ c x a = 0 A
• a,b +b,c +c,a =0 B
• a,|a xc| =0 C
• a+b+c =0 D

• 
  A
• 
  B
• 
  C
• 
  D

Let A,B, and C be any sets such that A∪B = A∪C and A∩B = A∩C then

• A≠ C A
• B = C B
• A = B C
• A≠ B D

The range of the function f : x→ y is defined by

• {x| y = f (x) ∀x∈ X ∧y∈y} A
• {(x,y) |y = f (x)∀x∈ X} B
• {y|y = f (x) ∀x∈ X ∧y∈y} C
• Y D

1st four terms of the expansion (1-x)^-2are

• 1 + 2x + 3x²+ 4x³ A
• 3x²+ 2x + 1 B
• 1 + 3x + 4x²+ 5x³ C
• None of these D

The5thand 13th terms of an A.P are 5 and-3 respectively The first term of the A.P is

• 1 A
• -15 B
• 9 C
• 2 D

The set of the first elements of the orders pairs forming a relation is called its

• Relation in B A
• Range B
• Domain C
• Relation In A D

Two cards are drawn at random from a well shuffled pack of cards. The probability that at least one of them is a face card is

• 3 / 17 A
• 5 / 17 B
• 7 / 17 C
• 9 / 17 D

The Domain of y = sin x is ______

• Set of real numbers A
• Rational B
• Irrational no. C
• None of above D

The set { {a,b} } is

• Infinite set A
• Singleton set B
• Two points set C
• Empty set D

• x = f(y) A
• y = f(x) B
• x = f(x) C
• y = f(y) D

Tangent is a periodic function and its period is ______

• 2π A
• 3π B
• π C
• 4π D

• 
  A
• In(x²- x + 1) + c B
• 
  C
• In(2x - 1) + c D

A,G,H are in

• A.P A
• G.P B
• H.P C
• None of these D

The area of a sector of a circular region of radius r is

• 2π r A
• π r² B
• 1/2πr² C
• π/6 D

If points A (6,-1), B ( 1,3) and C (x,8) are such that AB=BC, then x =

• 3,5 A
• -3,5 B
• 3,-5 C
• -3,-5 D

• Additive property in R A
• Multiplication property in R B
• Cancellation property in R C
• Distribution property in R D

(A ∩ B)c =

• A∩ B A
• (A ∪ B)c B
• Ac∪Bc C
• Φ D

n(n - 1) (n - 2) in factorial form is

• 
  A
• 
  B
• 
  C
• 
  D

A statement which is already false is called

• Tautology A
• Contrapsitive B
• Absurdity C
• Universal quantifiers D

• 
  A
• 
  B
• 
  C
• 
  D

• 8 A
• 1/56 B
• 56 C
• None of these D

A kite flying at a height of 67.2 m is attached to a fully stretched string inclined at an angle of 53 to the horizontal, the length of the string

• 62m A
• 82m B
• 73m C
• 57m D

If f(x) = (-x)²then f(-2) is

• 0 A
• 2 B
• -4 C
• 4 D

Cos (cos4π/3)=

• π/2 A
• π/3 B
• 2π/3 C
• -π/3 D

The angle of elevation of the top of a tree from a point 17 meters from is foot is 42^𝜊The height of the tree is

• 12m A
• 21m B
• 17m C
• 15m D

∫x sin xdx is equal to:

• sin x/x + cos x A
• sin x - cos x/x B
• x cos x + sin x C
• - x cos x + sin x D

Which of the following sets has closure property w.r.t. addition

• { 0 } A
• { 1 } B
• { 0, -1} C
• { 1, -1} D